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If the conjugate of $(x+i y)(1-2 i)$ is $(1+i)$, then
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Verified Answer
The correct answer is:
$x+i y=\frac{1-i}{1-2 i}$
We have,
Conjugate of $(x+i y)(1-2 i)$ is $1+i$.
i.e. $\quad(x-i y)(1+2 i)=1+i$
$\Rightarrow \quad x-i y=\frac{1+i}{1+2 i}$
Taking conjugate both sides, we get
$$
x+i y=\frac{1-i}{1-2 i}
$$
Conjugate of $(x+i y)(1-2 i)$ is $1+i$.
i.e. $\quad(x-i y)(1+2 i)=1+i$
$\Rightarrow \quad x-i y=\frac{1+i}{1+2 i}$
Taking conjugate both sides, we get
$$
x+i y=\frac{1-i}{1-2 i}
$$
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